Determining the relation between two matrices satisfying given conditions.

Prove that $1-\frac{\sin(x)}{x} < x^2/2$ for $x \in (0, \pi/2)$

Bound on remainder for vector valued Taylor series

The monoid of fractions associated with the submonoid of cancellable elements of a commutative monoid E

What's the size of an angle in a triangle with sides $\sin(x), \cos(x),$ and $\tan(x)$?

If $a^2>b^2$ prove that $\int\limits_0^{\pi} \frac{dx}{(a+b\cos x)^3}=\frac{\pi (2a^2+b^2)}{2(a^2-b^2)^{5/2}}$.

Which group is given by $\begin{pmatrix} e^{i\theta}&x\\0&e^{-i\theta}\end{pmatrix}$?

Is the endomorphism ring of a module over a non-commutative ring always non-commutative?

Real numbers inequality

What is the maximum value of $\frac{7x+2y}{2x+2}+\frac{3x+8y}{2y+2}$ while $0≤x,y≤1$

Six letter words from "MONSTER"

Prove $\sum_{\text{cyc}}^{}\sqrt[3] {1+2ac} \le 3\sqrt [3] {3}$.

How to prove $\forall k \exists y \forall x (x < y \Leftrightarrow \forall n (n < x \Rightarrow n < k))$?

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